Revealing consistent patterns and intrinsic mechanisms of subway systems via relative influence

Subway systems play a vital role in facilitating mobility within cities. However, the complex, nonlinear interactions between subway stations are difficult to capture using traditional approaches, which typically focus on static network structures or absolute passenger flow. These methods fail to adequately address the dynamic nature of subway systems and hinder cross-city comparisons. In this study, we integrate perspectives from dynamics and system science to quantify the relative influence between subway stations, accounting for both network connectivity and dynamic characteristics. This approach effectively eliminates biases related to city scale, allowing for meaningful cross-city comparisons. Additionally, we develop a simulation model that links individual travel behavior with collective-level phenomena, shedding light on the intrinsic mechanisms governing passenger flow. By analyzing relative influence, we define a station importance metric that reveals the functional roles of stations within the network. Empirical analyses of subway systems in Beijing, Chongqing, Nanjing, and Suzhou demonstrate consistent patterns in relative influence distributions across cities and time periods. These patterns align with a time-based, two-step preferential attachment mechanism governing passenger travel. A comparison of our proposed station importance metric with traditional centrality measures further validates its effectiveness. This research provides valuable insights into subway network operations, contributing to the optimization of system resilience and management strategies.